Wash and cut broccoli, carrots, bell peppers, mushrooms, or any other veggies that you want to use into bite-sized pieces and set aside.
Cook the yaki udon noodles according to package directions. (This usually allows them to soak in hot water for about 3 minutes.)
Combine all stir-fry sauce ingredients in a bowl (or large measuring cup), stir well, and set aside.
Place a large skillet or wok over medium heat, add 2 Tbsp of oil allow it to heat for about 1 minute, then add the chopped veggies, and sauté for about 3 minutes until tender.
Add the hot cooked udon noodles to the veggies. Then stir up the stir-fry sauce again (to ensure the starch is evenly distributed) and pour it over the noodles and vegetables.
Stir constantly for about 1-2 more minutes until the sauce thickens and coats the veggies and noodles. Serve hot.
Notes
You can add 1- 2 tablespoons of sesame oil to the stir-fry sauce for more flavor if you wish or simply stir-fry the veggies in sesame oil.
If you choose to add sesame oil to the stir-fry sauce do so after the cornstarch has dissolved or it will stick to the oil and get clumpy.
Be sure to cook the sauce until it starts to bubble and gets thick, translucent, and glossy.